Preheat the oven to 425°F (220°C).
Place the quartered red potatoes on a baking sheet. Drizzle with 1 tablespoon olive oil, sprinkle with salt, black pepper, dried thyme, and dried rosemary. Toss to coat evenly.
Add the sliced carrots, red bell pepper, and zucchini to the baking sheet with the potatoes. Toss again to combine.
Roast the vegetables in the preheated oven for 25 to 30 minutes, stirring halfway through, until tender and lightly browned.
While the vegetables roast, bring a large pot of salted water to a boil. Add the quartered potatoes and cook for 15 to 20 minutes until tender when pierced with a fork.
Drain the potatoes and return them to the pot. Add the butter, minced garlic, and whole milk. Mash until smooth and creamy. Season with salt and black pepper to taste. Keep warm.
Heat a large skillet over medium heat. Add the turkey sausage links and cook for 12 to 15 minutes, turning occasionally, until browned on all sides and cooked through (internal temperature should reach 165°F or 74°C).
To serve, divide the garlic mashed potatoes and roasted vegetables among four plates. Place the cooked turkey sausage links on top or alongside the vegetables.
Garnish with chopped fresh parsley and serve immediately.